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CHAPTER 1
1.1 to 1.41 - part of text
1.42
(a) Periodic: Fundamental period ¡ë 0.5s (b) Nonperiodic (c) Periodic Fundamental period ¡ë 3s (d) Periodic Fundamental period ¡ë 2 samples (e) Nonperiodic (f) Periodic: Fundamental period ¡ë 10 samples (g) Nonperiodic (h) Nonperiodic (i) Periodic: Fundamental period ¡ë 1 sample
l.43
¥ð 2 y ( t ) ¡ë ? 3 cos ? 200t + ? ? ? ? 6? ?
2 ¥ð ¡ë 9 cos ? 200t + ? ? 6?
9 ¥ð ¡ë cos ? 400t + ? 1 ? 2 3? 9 (a) DC component ¡ë -2 9 ¥ð (b) Sinusoidal component ¡ë cos ? 400t + ? ? 2 3? 9 Amplitude ¡ë -2
1
200 Fundamental frequency ¡ë Hz ¥ð
1.44
The RMS value of sinusoidal x(t) is A ? 2 . Hence, the average power of x(t) in a 1-ohm resistor is ( A ? 2 ) ¡ë A2/2.
2
1.45
Let N denote the fundamental period of x[N]. which is de?ned by 2¥ð N ¡ë §Ù The average power of x[n] is therefore 1 2 P ¡ë - ¢² x [ n ] N 1 ¡ë N
n¡ë0 N -1 N -1
¢²A
n¡ë0
2
A ¡ë N
n¡ë0 2 N -1
2 2¥ðn cos ? - + ¥õ? ? N ? 2